Comic Irony
Basically, this is when any irony is used in a humorous way. Comic Irony can be situational, historical, or verbal. It just has to make you laugh.
Historical irony
When history is seen through modern eyes, there often appear sharp contrasts between the way historical figures see their world's future and what actually transpires. For example, during the 1920s The New York Times repeatedly scorned crossword puzzles. In 1924, it lamented "the sinful waste in the utterly futile finding of words the letters of which will fit into a prearranged pattern." In 1925 it said "the question of whether the puzzles are beneficial or harmful is in no urgent need of an answer. The craze evidently is dying out fast." Today, no U.S. newspaper is more closely identified with the crossword than The New York Times.
In a more tragic example of historical irony, what people now refer to as "The First World War" was called by H.G. Wells "The war that will end war",[35] which soon became "The war to end war" and "The War to End All Wars", and this became a widespread truism, almost a cliche. Historical irony is therefore a subset of cosmic irony, but one in which the element of time is bound to play a role. Another example could be that of the Vietnam war, where in the 1960s the U.S. attempted to stop the Viet Cong (Viet Minh) taking over South Vietnam. However it is an often ignored fact that, in 1941, the U.S. originally supported the Viet Minh in its fight against Japanese occupation.[36]
Socratic Irony
Pretending not to know something so that your students can learn from your feigned ignorance.